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A-A124 696 IMPROVEDCSIGNAL CONTROL AN ANALYSIS OF THE E SUFAEANCO~ AR OCETS F CHWq OGHTPATTERSON AFB OH SCHOOL OF ENGI. K LFSHER
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AFvr/GEO/EE/82D-3
IMPROV7) SIGNAL CONTROL: ANANALYSIS OF THE EFFECTS OF
AUTOMATIC GAIN CONTROL FOR OPTICALSIGNAL DETECTION
THESIS
IAFIT/GEO/EE/82D-3 Kirk L. FisherLt USAF 9
FEB2 2 9k
* Approved for public release; distribution unlimited
AFIT/GEO/EE/82D-3
IMPROVED SIGNAL CONTROL: AN ANALYSIS OF THE EFFECTS
OF AUTOMATIC GAIN CONTROL FOR OPTICAL SIGNAL DETECTION
THESIS
Presented to the Faculty of the School of Engineering
of the Air Force Institute of Technology
Air University
in Partial Fulfillment of the
Requirements for the Degree of
Master of Science
b y
Kirk L. Fisher, B.S. 7
Lt USAF jGraduate Electro-optics
December 1982
Approved for public release; distribution unlimited.
Preface
Currently, research is being conducted by the Air Force
Wright Aeronautical Laboratories to replace copper wire data
links on board aircraft with an optical fiber system. The
optical fibers are to be used to transmit information from
sensors, which are placed throughout the aircraft, to a cen-
tral receiver. Because of the attenuation in the cable and
the optical to electrical conversion process, the signal in-
curs variations causing the detection accuracy to decrease.
This report is to analyze the effects of adding an automatic
gain control (AGC) circuit to provide amplification of the
signal and control to the signal variations.
I would like to thank my advisor, LtCol R. J. Carpinella,
of the Air Force Institute of Technology, for his guidance
towards the completion of this study. I would also like to
express my gratitude to my fellow classmates, family, and my
fiancee, Lynette Pray, for their support and inspiration
throughout the extent of this study. And finally, I wish to
acknowledge my thanks to my typist, Mrs Ruth Walker.
Kirk L. Fisher
ii
Contents
Page
Preface.......................... .. .. ...... .. .. . . ...
List of Figures......................v
List of Tables......................vii
List of Symbols........................viii
Abstract..........................x
I. Introduction.....................Background...................Problem.......................2Scope.......................4Assumptions...................5Approach and Presentation.............5
11. Performance Parameters...............7Optimum Decision Criteria...........7Objective of Adding an AGC..........12
III. Receiver Model...................13Photodetector Model...............13
Ideal Photodetector...........14Non-Ideal Photodetector..........16
AGC Model...................17VGA....................1GCP...................19
* Basic Configurations..........19Steady-State Analysis..........21
IV. Computer Simulation.................25Photodetector Algorithm............25
Simulation of a Poisson CountingProcess...............25
Simulation of the PhotodetectorOutput Voltage............27
AGC Algorithm................32Simulation of the AC .......... 33Steady-State Response Curve.......34Teat Signal Response...........35
Receiver Algorithm...............37
V.* Results..........................43Receiver vith an*IAQC...............43
ii4
Simulation Parameters............43Analysis...................45
Receiver with an AG...............56Simulation Parameters............56Analysis...................57
Receiver with a Dual AGC...........63
VI. Conclusions and Recommendations............72
Bibliography.........................71
Appendix A: Graphs of Various AGC Responses.........72
Appendix B: Computer Program...............
iv
List of Figures
Figure Page
1 Received Optical Signal ...... ............ 3
2 Deterministic Binary Signal of the Photodetector 8
3 Photodetector Configuration .. .......... 14
4 VGA ......... ....................... 1
5 Single Loop AGC Configuration .. ......... 20
6 Complex AGC Configurations ... ........... . 21
7 Single Loop AGC ...... ................ 22
8 Steady State Response Curve .. .......... 24
9 Block Diagram of the Counting Process Algorithm 27
10 Simulation of the Poisson Counting Process . 28
11 Photodetector with Switch Impementation . . . 29
12 Block Diagram of the AGC Algorithm ... ....... 34
13 Simulated Steady State Response Curve ..... 36
14 Steady-State Graphic Analysis of the Test Signal 38
15 AGC Input Test Signal .... ............. 39
16 AGC Output with Test Signal Input . ....... 40
17 Input Optical Signal for a Receiver with an IAGC 45
18 Graphic Analysis of the IAGC Response ..... 46
19 IAGC Input ....... ................... .. 49
20 IAGC Output ....... .................. 50
21 Improvement of the SNR by the IAGC ........ .. 52
22 Worst Case Signal ..... ............... 54
23 Approximation to Describe Signal Fluctuations 56
v
-.- o
24 Graphic Analysis of the ACC Response ....... 58
25 Input Optical Signal for a Receiver with an AGC 59
26 AGC Input.....................60
27 AGC Output.....................61
28 D~ual AGC Output..................64
Vi
List of Tables
Table Page
I Example of Photodetector Simulation Parametersfor Various Data Rates .... ............ 31
2 Estimate of the Probability of a Bit Error for anInitial Signal (binary one) Using an IAGC . . . 53
3 Estimate of the Probability of a Bit Error for the"Worst Case" Signal Using an IAGC ... ....... 55
4 Estimate of the Probability of a Bit Error for the"Worst Case" Signal Using an AGC . ...... 62
5 Estimate of the Probability of a Bit Error for the"Worst Case" Signal Using a Dual AGC (A =10000) 665
6 Estimate of the Probability of a bit Error for the"Worst Case" Signal Using a Dual AGC (Xs=5000) 67
vi
List of Symbols
A - effective area of the photodetector
A - constant gain amplification factor
b - bias voltage
B - bandwidth of counting process
C - capacitance
f - optical frequency
fs sampling frequency
Go - AGC gain parameter
hf - energy per photon
q - charge of an electron
R - resistance
TB - bit period
T - frame periodf
T - switching period
a - AGC control parameter
q - quantum efficiency of photon to electron conversions
"I - binary "one" given in terms of the rate of electronemissions
10 - binary "zero" given in terms of the rate of electronemissions
ID - constant rate of thermally emitted electrons
1S - constant rate of photon to electron conversions
iSD - S A D
h(t) impulse response
11(f) - ours ,r transform of h(t)
viii
--.._ ... ... ... ... ........ ....... .. ... .......- ------
U(r,t) - spatial and time representation of optical signal
P(t) - optical power
p(t) - power density
Xp (t) - rate of photons striking the detector surface
(t)- rate of electrons emitted from the detector
N(t) - count process
-counting vector
i(t) - photodetector output current
x(t) - photodetector output voltage of AGC input voltage
y(t) - AGC output voltage
g(t) - AGC gain
VC (t) - AGC control voltage
6(t) - unit delta function
u(t) - unit step function
Pr(error) - probability of bit error
DZI - decision criteria [Ref 6]
D
NJ (x) - product of x. termsiI
- indicates convolution
ix
AFIT/CEO/EE/82D-3
Abstract
This paper is to analyze the effects of an automatic gain
control (AGC) in an optical receiver system. The intent of
using an AGC is to improve the performance of the receiver.
The received signal is Manchester encoded and contains
fluctuations caused by transmission attenuation. In the con-
version from an optical signal to an electrical signal, the
photodetector produces shot noise. The purpose of the AGC
will be to amplify the photodetector signal, control signal
fluctuations, reduce shot noise, and improve detection ac-
curacy.
Using this criteria, the effects of the AGC in the
receiver was examined. But because of the non-linearities
associated with an AGC, an analytical analysis can not be con-
ducted. Therefore, the receiver was simulated on the com-
puter. This paper describes the models and algorithms used to
analyze the receiver. Through the simulations, the receiver's
performance with an AGC is compared to the performance without
an AGC.
Because of the limited time for the analysis, only three
specific AGC's were examined. The first AGC studied is clas-
sified as an instantaneous AGC (IAGC) followed by an analysis
of a common AGC. The final AGC to be investigated is a dual
AGC which is an AGC cascaded to an IAGC.
x
IMPROVED SIGNAL CONTROL: AN ANALYSIS OF THE EFFECTS OF
AUTOMATIC GAIN CONTROL FOR OPTICAL SIGNAL DETECTION
I. Introduction
Background
In recent years the application of optical fibers in com-
munication systems has increased significantly. Technological
developments have enabled low loss optical fibers to replace
copper wire communication links. Improvements were made in
laser diodes and LED's to achieve higher optical power out-
puts. Because of the higher output powers and low loss
cables, the distance between repeaters can be increased,
thereby, reducing construction cost. Construction costs were
also decreased and the construction simplified by improved
techniques and hardware for the interfacing and the splicing
of optical fibers. These are just a few of the advancements
which have contributed to the feasibility of an optical fiber
communication system and to its resultant growth.
The practicality of an optical fiber communication system
explains the current growth and increased usage, but the in-
herent advantages of the system prompted the initial interest
and research. The most important attribute is that more in-
formation can be transmitted through optical fibers than
through copper wire. Currently, Gigabit data rates have been
obtained by using single mode fibers. Optical cables are also
immune to electromagnetic radiation. No special shielding is
required to protect them against high electric or magnetic
fields. The fibers are lightweight and pose no hazard to fire
or electrical shock. Because of these advantages and the
technological developments, optical fibers have become a cost-
effective replacement for copper wire; and optical fiber com-
munication systems are being implemented in many new projects.
Problem
One such project is to implement an optical fiber data
link on board an aircraft. The optical cables would carry
information from several sensors to a central receiver. The
sensors are placed at various positions throughout the air-
craft. Each sensor will transmit a Manchester encoded optical
signal via an optical fiber. Because the signals must travel
different path lengths to reach the receiver, the attenuation
losses will cause the optical power level to fluctuate between
the signals. At the receiver several bits of information from
each signal will be observed for one frame period (Tf). Thus,
the received signal (see Figure 1) will be a Manchester en-
coded optical signal with fluctuations in the power level
depending on which sensor is being observed.
2
" 0
T, ZT6 3 b r. S '7j i
Figure 1. Received Optical Signal
The received optical signal is then converted into an
electrical signal by a photodetector. Because of the fluctua-
tions in the received signal, the detector's output signal
will vary over a wide dynamic range. The photodetector signal
will also incur variations caused by the dark current and shot
noise which are inherent to the photodetectors. The shot
noise is used to describe the randomness associated with the
detector's generation of an electrical signal. The dark cur-
rent is a product of thermally emitted electrons flowing from
the detector. The dark current, shot noise and signal fluc-
tuations complicate the process of reconstructing the informa-
tion sent.
For the particular signal being studied, the information
is digitally encoded and is extracted by a decision circuit.
The decision circuitry determines whether a binary "one" or
?3
LI
"zero" was sent based on '-he photodetector's output. To
increase the accuracy of the decision process, an automatic
gain control (AGC) circuit will be placed in between the
photodetector and the decision circuitry. The purpose of the
AGC will be to amplify the detector signal and to auto-
matically adjust its gain to reduce signal variations,
thereby, hopefully improving the accuracy of the reconstruc-
tion.
In this paper a detailed analysis will be conducted on
the receiver to investigate the effects of an AGC in an op-
tical receiver. Because of the non-linearities associated
with an AGC, an analytical analysis of the receiver becomes
very complicated. Therefore, an empirical analysis will be
conducted using a computer to simulate the receiver. Through
the use of the computer, the effects of the AGC on the detec-
tor signal, the signal to noise ratio, and the probability of
bit errors will be examined.
Scope
Because of the limited time to conduct an analysis, only
three AGC's will be studied. The first AGC to be analyzed
will be an instantaneous AGC (IAGC), followed by an analysis
of a common AGC. Both AGC's employ a single loop feedback
configuration to provide the gain control. They both also
have a gain characteristic which is an exponential function of
the control voltage. The final AGC to be studied will be a
dual AGO, which is a cascaded combination of an IAGC and an
I :,: e~~~~~~~~ :~~4 -- . . . -'^"" i .." . . .. . . . .. . .
AGC.
The photodetector will be a non-amplifying photodiode,
such as a p-n or a p-i-n diode. The effects of avalanche
photodiodes will not be considered in this analysis.
Assumptions
The photodetector will be illuminated solely by the Man-
chester encoded optical signal. The detector will be com-
pletely enclosed to eliminate the effects from the background
radiation. The received optical signal will be undistorted
except for the attenuation caused by the transmission through
the optical fiber. The signal is also assumed to be spatially
coherent, so that the optical power can be written as
P(t) - fi A U(,t) dr = p(t) A (I)
where
U(7,t) - spatial and time representation of the signalpower density
p(t) - time varying power density
A - area of the detector
All noises will be neglected except for the shot noise and
dark current. The timing of the electrical circuit will be
exactly synchronized with the optical signal.
Approach and Presentation
Before any analysis of the receiver is conducted, the
performance parameters of the receiver will be defined. Based
on the photodetector output, an optimum decision rule is
developed to minimize the probability of a bit error. The
5
effects that the AGC has on the probability on error and the
signal fluctuations will be used to assess the AGC's
performance. The objective of adding an AGC will be to am-
plify the detector output, eliminate the signal fluctuations
and to decrease the probability of a bit error.
With these objectives in mind, the mathematical models
are developed to describe the receiver. These models need to
represent the physical devices as accurately as possible to
obtain valid results. From the mathematical models computer
algorithms will be developed. Some simple simulations of the
photodetector and AGC will be conducted to test the validity
of the computer programs.
Using these computer programs, the effects of the three
specific AGC's on the photodetector signal will be analyzed.
The AGC~s response to the detector's output will be obtained
by plotting the first and second order statistics of the AGCs'
output. The effects of the AGC on the probability of error
will also be examined. From this analysis conclusions can be
drawn as to the effectiveness of an AGC in an optical
receiver.
IT. Performance Parameters
The purpose of a receiver is to reconstruct as accurately
as possible the information which was transmitted. Unfor-
tunately, the signal becomes distorted during the transmission
and the reception. The distortion introduces error in the
reconstruction of the information sent. For the digitally
encoded signals, the information is transmitted in binary
form. Each single piece of binary information sent is re-
ferred to as a bit and is represented by a "one" or "zero".
Distortion of a digital signal causes incorrect decisions or
bit errors to be made. In the following section the
probability of a bit error is minimized through the develop-
ment of an optimal decision rule.
In the last section of this chapter the objectives of
adding an AGC will be discussed. These objectives will
specify the parameters to assess the performance of the AGC's.
Optimum Decision Criteria
For the digital signals which are being analyzed, the
binary information is determined by the position of the pulse.
This type of digital encryption is called pulse position
modulation (PPM). A binary "one" will be assigned to the op-
tical pulses which occur during the first half of a bit period
(TB), and a binary "zero" to the pulses which occur in the
7
second half of the bit period.
At the receiver these optical pulses are converted into
an electrical signal by a photodetector. The electrical sig-
nal, that is generated by the detector, is no longer a deter-
ministic signal; but becomes a weighted Poisson counting
process (will be proven in the next chapter). Because the
signal is now a random process, errors will occur in the deci-
sion process. Fortunately, the rate of the counting process
is proportional to the power density of the optical signal.
Thus, the binary signals can be represented by the rates of
the counting processes (see Figure 2). An optimum decision
rule will be developed to extract this deterministic signal
from the Poisson counting process, N(t).
A - rate of photon toelectron conversions
I- rate of thermallyX emitted electrons
ASOSAS~
I Io
0 0
Figure 2. Deterministic Binary Signal of the Photodetector
To obtain a decision rule, the Poisson counting process
is to be equivalently written in a vector form. This vec-
8
torization is accomplished by sampling the counting process,
N(t), at a rate defined by: r.f > 2B (2)
where
BN = the bandwidth of the counting process
This sampling scheme produces a count vector given by:
k = (klpk 2 ,....k ) (3)
where
k = N(t.) - N(t.j-1 for j-1,2,...,J
J = Tfs
The probability of a count k occurring is defined by (Ref
3:205+):
Pr(k/Xij) = [(XijAt) j ] / k.! (4)
where
At t - tj. I
A = rate of the i th signal during the interval
tJ t - 1
Since the probabilities of each sample count are independent,
the probability of the count vector can be written as:
J kj X ijAt
Pr(k/Ai) R [(AiiAt) e ] / (5)J=I
Based on these probabilities a decision rule can be developed.
The optimum decision rule for minimum probability of er-
ror can be derived from the maximum a posteriori (MAP) deci-
9
sion criteria. The MAP decision criteria is defined as:
DI
A(r) = P(XI /k)/P( o/k) ] Z (6)DO
where
A(r) = likelihood ratio
P(X /k) = probability that the rate is Xi given the
observed vector k
By applying Bayes rule, the MAP criteria can be equivalently
written as:
rPr(k/1 ) Pr() Pr(k) >IA(r) = - < ( 7)wh re = rPr(k/.0 ) Pr(Xo)1 / Pr(k) D (
where
Pr(k/X i) = defined by eqn (5)
Pr(X.) = priori probabilities of the given rate X.
Pr(q) probability of the vector k occurring
Assuming equal priori probabilities and substituting eqn (5)
into eqn (7) produces:
J kJ e -k D
A(r) = J1 (8)
J k -XOjt DR X At) J e / k
Since the logarithm is a monotonic increasing function, an
equivalent MAP rule is:
10
Jl
lnA(r) - [k. 1nl~ tJJ
Z [k. lnA0 ,At X0 At] < 0 (9)j=1 o Do
By separating the summations and correctly defining the limits
produces constant rates for each of the smaller summations.
This causes eqn (9) to be rewritten as:
J12 J£ [kj AsDAt - AsDAt] E [k. ln DAt - ADAt]
j=1 j=J/2+1 D
J/2 J DIE[kj iD At + AD At]- Z [k. lnASDAt - ASDAt] < 0 (10)J1 jJ/2+1 D
By rearranging the terms and simplifying, eqn (10) reduces to:
J12 J DZ k. - Z k. >1 0 (11)J=1 jJ/2+1 D 0O
Thus, the optimum decision rule compares the count at the end
of the first half of a bit period with the counts which occur-
red in the second half of the bit period. Writing this in
terms of the actual counting process produces:
D II
N(TI2) N N(T) - N(T/2) (12)D O i
The probability of error is given by:
Pr(error) - Pr(N(T/2)>N(T)-N(T/2)/ XO)P( A) +
112 Pr(N(T/2)-N(T)-N(T/2)/ )P( AO) (Pr(N(T)-N(TI2)>N(TI2)/ )P( +
1/2 Pr(N(T)-NCTI2)-N(TI2)I xl)P() (13 )
11
I
Substituting in the Poisson probability densities eqn (13)
becomes (Ref 3:220):
0 -)k -DT/2
Pr(error) = D - E [xDT/2 e 1/k!]i=O k=O
[( sDT/2)i eS i!] (14)
According to the MAP decision criteria, the decision rule
produces the minimum probability of error (Ref 6:42). The
decision rule was developed assuming constant optical power
densities of all the received pulses. But the decision rule
that was derived was found to be independent of the rates.
Since the rates are proportional to the optical power den-
sities of the pulses, the decision rule will not be effected
by signal fluctuations.
Objective of Adding an AGC
In the previous section an optimum decision rule was
developed for the detector signal. An AGC is now added to the
optical receiver. The purpose of the AGC will be to amplify
the detector output, eliminate the signal fluctuations and
minimize the probability of bit errors. These objectives will
be the criteria from which the performance of the AGC's will
be judged.
12
12 --
III. Receiver Model
In this chapter, the mathematical models of the receiver
will be developed. These models will form the basis for the
computer simulations and the analysis. Therefore, these
models must accurately represent the actual physical devices.
The model for the photodetector will be described in the first
section of this chapter, and in the last section, models for
the AGC will be presented.
Photodetector Model
The photodetector model must accurately describe optical
to electrical conversion process. To accomplish this the
photodetector will, at first, be described as an ideal
photodetector and then as a non-ideal detector. The ideal
photodetector will be defined as a detector in which elec-
trical output is present only when the detector is being il-
luminated by an optical source. In reality, a small amount of
electrical output will be present even when no optical power
is applied; this will be considered in the non-ideal case.
For either model the detector will be followed by an RC
filter (see Figure 3). R is the parallel equivalent of the
internal resistence losses of the detector and an external
resistor, and C is the parallel equivalent of the internal
capacitance losses and an external capacitor. The detector
13
output current is i(t) and x(t) is the output voltage of the
filter.
R U'C
Figure 3. Photodetector Configuration
Ideal Photodetector. An ideal photodetector will produce
an electrical output only when the detector is being il-
luminated by an optical source. The photons emitted by the
source will, strike the surface of the detector at a rate
defined by:
A p(t) p(t)A / hf 0 (15)
where
p(t) irradiance or incident power density
A = effective area of the detector
hf 0 = energy of a photon
If a photon has sufficient energy, it will excite an electron
on the surface of the detector into the conduction band. The
excited electron will then be emitted out of the detector.
14
b
This process will loosely be defined as a photon to electron
conversion.
As more photon to electron conversions occur, a detector
output current can be described as:
Ii(t) = q Z 6(t-ti) (16)
i=O
where
q charge of an electron
t. = time at which a photon to electron3. conversion occurred
This current will flow through the filter to produce an output
voltage, x(t), defined by the convolution integral:
x(t) =fti(t)h(t-T) dT (17)
where
h(t) = I/C e-tIRC = filter impulse response
or, equivalently:
X(t) C i(T)e(t)/R dT (18)
If the period of observation is much smaller than the RC time
constant, an approximation can be made to eqn (18) which
results in:
x(t) = I/C f i(T) dT
Substituting in eqn (16) for the current and integrating
produces:
I
x(t) - q/C E u(t-ti) - q/C N(t) (20)i-0
15Ip1
The output voltage is now modelled as a weighted counting
process, counting the electrons emitted from the detector.
Because the event times (t i s) of these photon to elec-
tron conversions occur randomly, the counting process is Pois-
son distributed. The rate of occurrence of the photon to
electron conversions is proportional to the rate of the
photons striking the surface of the detector. This rate is
defined as:
X(t) = (np(t)A) / hf 0 (21)
where
n - quantum efficiency of the photon toelectron conversions
Because the rate is time varying, the output current and
voltage become inhomogeneous Poisson processes in which the
statistics are known (Ref 8:432+) in terms of the rate.X(t).
Non-ideal Photodetector. In this section the photodetec-
tor model will be expanded to take into account the dark cur-
rent, which is present whether or not the detector is being
illuminated. The dark current is a result of thermally ex-
cited electrons reaching the conduction band. Therefore, like
the ideal model, the dark current is represented by:
Jid(t) - q E d(t-tj) (22)
J-0where
t - time at which a thermally excited electronenters the conduction band
16
The event times (t.'s) also occur randomly with a constant
rate of occurrence AD (assuming no significant temperature
variations).
Including dark current into the model, the current output
becomes:
i(t) = is (t) + id(t) (23)
where
i (t) signal current
id(t) = dark current
Substituting eqn (16) and eqn (22) into eqn (23) produces:
I Ji(t) = q[ E 6(t-ti) + Z 6(t-t.)] (24)
i=O j=O
and integrating to get the output voltage:
I Jx(t) = q/C E E u(t-t.) + E u(t-t.)] (25)
i=O J=o
Again the statistics are known in terms of the rates A(t) and
AD"
The output voltage given by eqn (25) will be the
mathematical model used to represent an actual photodetector
output. And as long as the approximation RC is greater than
the observation period, this model will accurately describe
the photodetector.
AGC Model
In this section several AGC models will be briefly ex-
amined and a steady state response for a specific AGC will be
analysed. For an analysis of other AGC's the reader is refer-
17
red to Senior (Ref 91. Much of the analysis on AGC's presen-
ted in this section follows the same approach developed by
Senior.
An AGC consists of two major components:
1) Variable Gain Amplifier (VGA)
2) Gain Control Processor (GCP)
The two components will be examined separately in the fol-
lowing sections. Then the various configurations which can be
derived from combinations of these two components will be ex-
amined briefly. In the last section a steady state analysis
will be conducted for a specific AGC.
Vnpvfou.I
• tpu4
conedo
Figure 4. VGA
VGA. The VGA is a three port amplifier in which the extra
port is used to control the gain of the amplifier (see Figure
4). The VGA is characterized by its gain to control voltage
relationship. Virtually every VGA can be classified as either
18
a linear VGA where the gain is represented as a function of
the vc(t) by:
g(t) - G - vc(t) (26)
or an exponential VGA in which the gain is defined as:
-v C(t) (27)
g(t) = GO e
where
a >
The discussion will be limited to these two VGA models. Other
VGA's are generally designed to perform special functions and,
therefore, will not be considered.
GCP. The GCP processes some portion of the signal to
provide a control voltage, vc(t), to the VGA. To keep the
analysis simple the GCP will be limited to the use of passive
filters, constant gain amplifiers, and constant biasing. With
this limitation the output control voltage, vc(t), is easily
defined as:
vCo(t) - A vei(t) * h(t) + b (28)
where
vci(t) = input voltage
A - constant gain of amplifier
h(t) - impulse response function of the passive filter
b - bias voltage
-= indicates convolution
Basic Configuration. By using various combinations of
the two components (VGA and GCP), numerous AGC models can be
19
constructed. The simplest AGC models are classified as the
single loop configurations (see Figure 5). It should be noted
here that each configuration does not represent one AGC model.
The configuration is used to classify a group of AGC models;
the actual AGC model depends on the component characteristics.
VGA pfinp VGA
GCPCIr
feedforward feedback
Figure 5. Single Loop AGC Configurations
The multi-loop configurations contain three or more com-
binations of the two AGC components. The multi-loop systems
are divided into two sub-divisions:
1) Compound Systems
2) Complex Systems
A compound system is two or more single loop configurations
cascaded together. A complex system includes everything which
can not be classified as single loop or compound systems.
Figure 6 shows two examples of complex systems.
20
Figure 6. Complex AGC Configurations
Steady State Analysis. The steady state response curve
is an important characteristic of an AGC. This curve can be
used to predict an AGC's response to any input. Also, for
single loop conf.igurations, a steady-state analysis can be
used to specify the AGC parameters. In this section a steady
state analysis will be developed for a common AGC.
For the analysis the VGA will have an exponential gain
characteristic and the GCP will be placed in a feedback con-
figuration. The filter in the GCP will have an impulse
response defined as h(t). This particular system is chosen
because it has a constant loop gain which provides greater
stability (Ref 12). An AGC is considered stable when the out-
put settles to a constant value after an abrupt change in the
input (Ref 9:14).
21
IL .
rii
Figure 7. Single Loop AGC
Using this model (see Figure 7), a steady-state analysis
of the AGC is conducted. The output of the AGC is described
by:
y(t) - x(t) g(t) (29)
Substituting in eqn (27) for the gain and A v(t) for the con-
trol voltage produces:
y(t) = x(t) G e-aAv(t) (30)0
Since the parameters A and a have the same effect on the out-
put, the parameter a will be absorbed into the parameter A.
Thus, the AGC output is given by:
y(t) - x(t) G 0 e- A v (t) (31)
where
v(t) - y(t) * h(t)
22
The steady state response is obtained by driving the AGC
with a constant amplitude input, k. After the initial tran-1
sients decay, a stable AGC will produce a constant amplitude
output, k For a constant output the filter response is0
defined as:
v(t) = k * h(t) (32)0
or, equivalently:
v(t) = k0 * H(O) (33)
where
H(O) = 41h(t)} If=O
Substituting in k for the output, ki for the input, and
k H(O) for the control voltage, eqn (31) becomes:
-Ak f0)ko = k G0 e o (34)
Eqn (34) is the steady-state response of the AGC and the
response curve (see Figure 8) is obtained by plotting ki ver-
sus k
This steady-state response can serve as a useful tool to
obtain the values of the AGC parameters G and A; provided the
input-output ranges are known. For the analysis, the input is
assumed to vary between kil and ki 2 . The output is to be
limited to the range ko to ko2 (see Figure 8).
23
0. 4 0. la.2.
Figure 8. Steady-State Response Curve
Substituting each pair of points into eqn (34) results in:
k iik 011e A k01/ 0 (35)
and
AI{(O)k ok k 0/ G (36)
ki2 ko2 e0
Taking the ratio of the above equations and solving for A
produces:
A = ln[(k 2 /kc1 (k0 /k2 ) [H~(O) (k02 .k 1) (37)
Once a value of A is determined, 0 0can be obtained by using
eqn (35) or eqn (36).0
24
IV. Computer Simulation
Because of the non-linearities of the AGC, an accurate
analytical analysis of the receiver would be very difficult
and complex. Or, if approximations are made to simplify the
analysis, the receiver would not be represented accurately.
Therefore, an empirical analysis was conducted and the
receiver simulated on the computer. This chapter describes
the process used to develop a computer program to simulate the
receiver.
Photodetector Algorithm
The photodetector models developed in the previous chap-
ter-easily conform to computer simulation. The first section
will describe the algorithm used to simulate the counting
process. The algorithm must then be modified to be able to be
implemented practically and still be able to accurately
represent the physical device. The last section deals with
the approach used to accurately simulate the photodetector
output voltage.
Simulation of a Poisson Counting Process. From the
results of the previous chapter, the photodetector output
voltage was mathematically modelled as a Poisson counting
process. In this section an algorithm to simulate the coun-
ting process will be presented.
25
. . . .. .. ... . .. .
For a Poisson counting process, the events occur at ran-
dom times. The time interval between two successive events
are also random and independent of any previous time interval.
To simulate the counting process, random numbers are generated
by the computer to represent the random event times. Using a
built-in program, random numbers which are uniformly
distributed from 0 to 1 are generated. The uniform random
numbers are then transformed into exponentially distributed
random numbers by [Ref 10:62]:
T -- in (u) / X (38)
where
= exponentially distributed random variable
u = uniformly distributed random number (0,I)
X - constant rate for the occurrence of events
The random number generated by eqn (38) is used to represent
the length of the time interval between two successive events.
By using the above procedure to produce the random time
intervals, a Poisson counting process is easily simulated.
The time at which the events occur is defined by:
t i = ti. I + T (39)
where ti - arrival time of the i th event
Ti - ith exponential distributed indom variable
26
Step 1Generate a uniform
randm nuberRepeat Steps 1-4
to generate a
Step 2 conting processConvert the uniformRandom number into
an exponentialrandom number [eqn 381 Step 4
I At the event time
~t. increment
Step 3 the count by 1Use the exponentialRandom number tocompute an eventtime ti [eqn 391
Figure 9. Block diagram of Counting Process Algorithm
The event times are continuously generated until the time ex-
ceeds a specified period of observation. The counting process
is initialized to zero at the beginning of the observation
period, and incremented by one at each time, t. A block
diagram of the algorithm is shown in Figure 9 and an implemen-
tation of this algorithm for various rates is shown in Figure
10. This algorithm will be the basis for the simulation of
the photodetector's output voltage.
Simulation of the Photodetector Output Voltage. The
counting process algorithm is used to simulate the Poisson
process, which mathematically models the detector's output
voltage. This model, which was developed in the previous
chapter, is defined by:
27
(0
'U) r
0ryS
LIz M
U
0k-4
Figure 10. Simulation of the Poisson Counting Process
28
b
I 3
x(t) q/C [ i~oU(t-ti) + j U(t-t.)] (25)
Each summation in eqn (25) represents a Poisson counting
process. In order to conduct the simulation, both Poisson
processes have to be homogeneous. The second summation in eqn
(25) is considered to be a homogeneous process, but the first
is inhomogeneous because of the time-varying optical signal.
Fortunately, the particular optical signal being studied
enables the first summation to be analyzed as a homogeneous
process.
Cx;)RI
Figure 11. Photodetector with Switch Implementation
To analyze the inhomogeneous process as a homogeneous
process, a switch is added to the photodetector model (see
Figure 11). The clocking period (Ts) of the switch is half
the bit period (Tb ) of the Manchester coded optical signal.
During the extent of the clock period, the output of the
29
detector will be observed. If the switch is synchronized with
the optical signal, the power density of the received signal
will remain constant during a switching period; and this will
produce a homogeneous counting process at the output. At the
end of a clock period the switch will temporarily short cir-
cuit the capacitor, thus, initializing a new counting process.
Using this switching scheme, the output voltage is modelled as
a periodic series of homogeneous Poisson processes.
To implement this model, the two counting processes are
simulated by the program developed in the previous section.
The two simulated processes are added and multiplied by q/C to.
produce the output voltage. The output is then sampled at
regular time increments, At, so that the output will be easily
integrated with the AGC simulation.
The parameters of the photodetector simulation are now
specified to realistically represent the output of a physical
detector. The parameter which has the most influence on an
accurate simulation is the rate (A) of the counting processes.
For an accurate representation, the simulation rates are re-
quired to be the same as the actual rates of the electron
emissions. For an ideal detector, the emission rates are
given by:
A = npA/hfo (21)
The time dependence was eliminated through the implementation
of the switch. The optical power of sources generally ranges
from 1 mw to 10 mw [Ref 5, Table 1] for infrared wavelengths.
30
Assuming all of the source's output power is detected, the
rate is calculated to be an order of magnitude of 1015/sec. A
rate of this magnitude is impracticable to implement directly.
A combination of two methods is used to increase the
feasibility of the implementation. The first approach is a
simple time scaling. Thus, the rate calculated above can be
equivalently written as 10 9 /.sec or 10 6 /nsec. This will not
cause the simulation to misrepresent the detector because the
signal, itself, is being observed in the scaled time units.
Table I
Examples of Photodetector Simulation Parameters
for Various Data Rates
MaxData Switch Max Elec Simula. M C (q/C)M RRate Period Emission Rate (e-/cnt) (V/count)(Ohms)
1 MBit 1psec 10 9 /usec 1000 106 IOuF 1.6xi0- IK
10 MBit 100nsec 108/100nsec 1000 105 2.OuF 8.0x0I- 9 IK
100 MBit 10nsec 107 /1Onsec 1000 104 2.OpF 8.0xi0 - 10 I0K
I GBit Insec 1O6 /nsec 1000 103 16nF 1.0xiO - 8 IK
10 GBit 100psec 105 /100psec 1000 102 5OpF 3.2xiO - 7 IOK
The second methoe is to have one count represent M electrons
emitted by the detector. The counting process is now weighted
by the factor M and the factor q/C. Since q/C is very small
in magnitude, the M can be easily "absorbed" into the factor
q/c without a misrepresentation of the detector.
31A _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _
I.
These two methods are applied to several different data
rates (see Table 1). The data rate determines the clock
period of the switch. The electron emission rate is then cal-
culated using eqn (21) (source optical power = 2mw) and scaled
to the same units of the clock period. A maximum rate for the
counting process simulation is determined for a practical im-
plementation. By dividing the actual electron emission rate
with the simulation rate, the factor M is found. A capaci-
tance is then chosen such that the factor (q/C)M is a small
quantity. With a known capacitance, the value of the resistor
is chosen to produce a long RC time constant compared to the
clock period (T s). A long RC time constant is required to
support the approximation that the detector can be represented
as a Poisson counting process. By using the two approaches
described above, a practical and accurate implementation of
the photodetector can be conducted.
AGC Algorithm
In this section an algorithm for the AGC simulation will
be presented. The algorithm to be developed represents the
single loop feedback system which was analyzed in the previous
chapter. Using this algorithm the simulated AGC will be
driven with constant amplitude inputs to generate a steady-
state response curve. This simulated curve is then compared
with a theoretical curve to verify the algorithm. The
validity of the simulation will also be tested using an am-
plitude modulated (AM) signal.
32
Simulation of the AGC. In the preceding chapter an
analysis was conducted on a single loop feedback system. From
the analysis an equation was developed to mathematically
describe the AGC. This mathematical model of the AGC is:
y(t) - x(t) G0 e- Av(t) (31)
where
v(t) = y(t) * h(t)
For the simulation the GCP filter is specified to be a simple
low pass filter. Thus, the control voltage is given by the
convolution integral:
v(t) = I/RC t y(T)e - (t - T ) / RC dT (40)0 y
where
R - filter resistance
C - filter capacitance
Developed from simple circuit analysis, the differential
equivalent of eqn (40) is:
C dv /dt - [y(t) - v(t)] / R (41)
Both equations accurately represent the filter, but eqn (41)
will be used to simulate the filter because of its simplicity.
Using numerical methods [Ref 4:189-190] eqn (41) is ap-
proximated by:
[v(tk+1 - v(tk)] / 4t - [y(t k ) - v(tk)] / RC (42)
or, equivalently:
v(tk+1) - Y(tk)(At/RC) + V(tk) (1+A t/RC) (43)
33
where
thtk = k sample time
At - tk+1 - tk
Sampling eqn (32) at the same rate produces:
y(tk) - x(t) ° -Av( k) (44)
Using these equations, the AGC is easily simulated on the com-
puter. A block diagram of the algorithm is shown in Figure
12.
Sample AGC Input,~ xik)
Step2Calculate an AGC Repeat steps 1-3
output y(t ) for the nextusing eqn (W4) sample interval
Step 3 1Predict an AGCcontrol voltage
V( tk+l )using eqn (43)
Figure 12. Block Diagram of the AGC Algorithm
Steady-State Response Curve. As mentioned earlier an
important characteristic of an AGC is its steady-state
response. To generate a response curve, the simulated AGC is
driven with constant amplitude inputs. By plotting the AGC
response (after transients decay) to these various inputs
produces a simulated steady-state response curve (age Figure
34
13). This is the exact result which would be obtained
theoretically for the same AGC parameters.
Test Signal Response. A test signal is used as input to
the AGC to verify the accuracy of the simulation. This test
signal is an amplitude modulated sine wave defined by:
xt) i + a sin 2!rfLt)(sin 2wfHt) (45)
where
f = carrier frequency
fL M modulation frequency
a - modulation index
The AGC will be designed to reduce the amplitude variations
caused by the modulation frequency and to pass the carrier
frequency unaffected.
Since the AGC is to reduce amplitude modulations, the GCP
must track the envelope of the signal. The GCP will consist
of a full wave rectifier and a low pass filter for envelope
detection. For the filter to pass only the envelope signal,
the RC time constant is required to be within the range FRef
13:97]:
1/f (< RC << I/f (46)
Since the carrier frequency is not affected by the AGC,
an approximate analysis can be conducted by working with the
envelopes and neglecting the carrier frequency. The most ac-
curate approximate method [Ref 9:67] is to use the steady-
state response curve as shown in Figure 14. The shape of the
35
orr I-
inl
I--)
w(Iz
w
>-
0
Figure 13. Simulated Steady-State Response Curve
(A-4,0 and G-100)
36
response curve is determined by the AGC parameters (A and G ).
The AGC parameters to produce a specific response curve
can be computed using eqn's (36) and (37). These equations
require knowledge of the range over which the input and output
signals vary. The AGC input signal (the test signal) varies
between 0.5 volts and 1.5 volts (for a modulation index a
0.5). The AGC ouput signal will be restricted to the range -
0.9 to 1.1 volts. With these values the AGC parameters A and
GO are calculated to be 4.5 and 100, respectively.
The AGC now can be simulated for comparison with the
graphical analysis. The input to the AGC is defined by eqn
(45) with a = 0.5, fL = 0.1/sec and fH = 10/sec (see Figure
15). The RC time constant of the low pass filter is I sec.
The AGC prrameters are A - 6.2 and Go M 100. The A was in-
creased to take into account a voltage drop across the filter.
The AGC output voltage as a result of the simulation is shown
in Figure 16.
Receiver Algorithm
The receiver algorithm is simply the integration of the
photodetector and the AGC algor'thms. With this algorithm the
receiver's response to an optical input can be simulated. In
this section a method will be developed to compute the
parameters to evaluate the performance of the optical
receiver.
To analyze the effects of the AGC, the receiver is more
appropriately described by the first and second order
37
LL41 10- - ir I q !
. _I -- ,-- -- - - . - . .. ... ,- \-
1-
cSO
. I I I III
T * --- -I ... -
Ii 1 C ___
Figure 14. Steady-State Graphical Analysis of the Test Signal
38
I -
MaS
Ca
I-A
Figure 15. AGC Input Test Signal (f =0. lIZ,fH.1. and a-0.5)
39
Q
ca
j s.. . . .2
El)*-'*-"-- ..... " -'. - --
r, CD . ....... -
F-a
iz%
A . '-IZ 3.- .,.
0- Cf4 ra. -
-'-A C-o~
0901 0800 0 8*- 0 IT(
Figur 16. ACC Ouptwt etSgaSnu A62 =0 nRC-1.0____
.. ,~n a40
statistics. To generate the statistics, the receiver is
simulated several times with the same optical input. After
the simulations, the mean of the signal for a sample time tk
is computed by using [Ref 8:245-246]:
Nk) -= [ilsi(tk)] / N (46)
where
' i= sample mean of the signal at the time tk
si(tk) the i th simulation of the signal at time tk
N = total number of simulations conducted
The signal variance is then obtained by using:
Nk = s2 (tk) = {iP,[s(tk) - si(tk)] 21 / N (47)
where
02ak = sample variance of the signal at time tk
From these statistics the effects that th'e AGC has on strength
of the signal and the signal fluctuations can be examined.
To study the effects that the AGC has on the detection
accuracy, an estimate of the probability of a bit error has to
be computed. The decision rule that minimizes the probability
of error compares the voltage (r1) at the end of the first
half of a bit period with the voltage (r2 ) at the end of the
bit period. This decision rule can be applied to both the
photodetector output and the AGC output which will be proven
in the next chapter. A bit error occurs if rI < r2 when a
binary one is transmitted, or if rI > r2 when a binary zero is
transmitted.
41
*
For the receiver simulations, the probability of error
can be computed by defining a random variable as [Ref 8:265-
266]:
1 if ri,<r 2 1 given a binary one transmitted
[if rli>r 2 1 given a binary zero transmitted
{1/2 if riir21(48)
0 otherwise
With this random variable, the probability of error is ob-
tained by using:
NPr c(error) - ( z) / N (49)
where
Pr (error) = computed probability of errorc
= mean of the random variables (zi)
The variance of the random variable is defined by:
S1(ziz)2] / N (50)
By using this variance and Tchebycheff's Inequality, the cer-
tainty of the estimate of the Prc(error) can be quantified.
Tchebycheff's Inequality is given by [Ref Papouliis:259-260]:
Prl PrA(error) - Pr c(error)l < 1 - az2 / (Ne 2 ) (51)
where
Pr A(error) - actual probability of error
The probability of error as well as the first and second order
statistics will be used to determine the performance of the
receiver.
42
h°-
V. Results
In this section an implementation of several optical
receivers will be conducted and the effects of the AGC's ex-
amined. A receiver with an "instantaneous" AGC (IAGC) will be
the first to be analyzed. An IAGC is a special classification
of an AGC. The IAGC's are designed to be more sensitive to
input changes, whereas the AGC's are designed to respond to
the slow fluctuation in the input amplitude (Ref 9: 81). Fol-
lowing the IAGC analysis a receiver containing an AGC will be
examined. The last receiver to be analyzed contains a dual
AGC, which is (for this study) an IAGC and an AGC cascaded
together.
Receiver with an IAGC
Because an IAGC is more sensitive to input changes, it
should respond to the changes caused by shot noise as well as
the signal fluctuations. The effects that the IAGC has on the
photodetector output will be analyzed in this section. This
analysis will be accomplished by computing the first and
second order statistics along with the probability of error.
Simulation Parameters. To conduct the analysis the
receiver models which were developed in the previous chapter
will be used. The power densities of the optical pulses being
received are arbitrarily chosen to vary over a 20 db
2 2range: 0.2w/cm to 2.0w/cm 2
. Using eqn (21) the rate of
43
photon to electron conversions will vary from 1014 to 1015 e-
/sec (Area-Imm 2 , nl0.1, and f = 3.2x10 1 4 ). The rate of ther-
mally emitted electrons is generally several orders magnitude
smaller than the signal rates and, therefore, was arbitrarily
chosen to be O13 e-/sec. With these counting rates and with a
giga bit baud rate, the simulation parameters for the detector
are given in table 1.
The AGC parameters, A and G can be determined by desig-
ning the IAGC to limit the output values to a range 20mV to
4OmV for inputs that vary between 0.4uV to 10.OuV. The output
range was "arbitrarily" chosen; although tradeoffs were made
to keep papameters, A and Go, realistic. The input values
were obtained from the photodetector's response. The 10.OUV
is the expected value of the detector at the end of a clock
period when the maximum optical signal is being received. The
minimum input value was determined by the MAP decision
criteria for an on-off keying digital signal. This MAP deci-
sion rule, based on the detector output, is defined as (Ref
3:216):
X(T) q/C N(Ts) < q/C Is Ta/ln(I+XS/ D) (52)DO
where
I S - rate of photon to electron conversionsS
D - rate of thermally emitted electrons.
Using the photodetector parameters, XD = 1013 and XS -014
(AS is the rate for photon to electron conversions correspon-
44
ding to minimum optical power densities) the optimum decision
threshold is computed to be 0.44V. Substituting these values
into egns (36) and (37), an A and a G0 were calculated to be
125 and 6x106, respectively.
The final parameter to be specified is the RC time con-
stant for the AGC feedback filter. As long as the inverse of
the RC time constant is large compared to the bandwidth of the
signal, the AGC will be able to respond to rapid changes in
the input. For the analysis RC = 0.O1nsec will be used.
1.6
t.2
0.8
0.4
T e 2T 3~ ToS To7 4 7 To7iST& :z.(Jensec)
Figure 17. Input Optical Signal for a Receiver with an IAGC
Analysis. With these simulation parameters, the effects
of an IAGC in an optical receiver can be studied. For the
analysis the reeived optical signal will be pre-defined (see
figure 17). The photodetector detector output for this signal
can be easily determined in terms of the first and second
order statistics. Using this detector output and the steady-
state response curve, the IAGC's response can be predicted
45
4 --- -00
I O I
'Oe4
-- --- --Fiur 18 GIahia Anlsso/h CRsos
46 I
(see figure 18).
The AGC response generated from the graphical analysis
indicates that the IAGC provides control to the changes in the
signal. The relative range over which the signal fluctuates
is reduced by the IAGC. This is readily apparent by comparing
signal peaks during the intervals at which the optical pulses
were received. The IAGC will also reduce the shot noise ef-
fects as evident from a decrease in the variance of the sig-
nal.
In the process of reducing changes in the signal, the
IAGC also distorts the detector signal. From this distorted
signal the digital information that was transmitted is to be
extracted. Before the addition of the AGC, the decision rule
to detect the information was defined as
D1x((21-1)T) < ((21)T (53)
D0
where
T s M switch period
2i Ts iTB = i th bit period
x(t) - photodetector output
Since this decision rule is optimal for the photodetector
voltage, applying the same decision rule to the AGC output
would be appealing. For the particular AGC's being studied,
the input-output characteristic (steady state response curve)
is a monotonically increasing curve producing a one-to-one
input-output relationship. Because of this one-to-one
47
relationship, the same decision criteria can be used for the
AGC output.
The analysis conducted thus far utilized graphical tech-
niques to describe the effects of an AGC. From the graphic
analysis, an IAGC's response to the a photodetector input was
predicted. The optimum decision rule for this IAGC response
was determined to be the same criteria that is used for the
detector output. The graphical analysis provides some insight
as to what the IAGC response will be, but can not be used to
predict the actual response.
To study the aynhmic effects of the IAGC requires the use
of a computer. Employing the algorithms developed in the
preceding chapters, a simulation of the receiver was conduc-
ted. The receiver's response to an optical input was obtained
using the simulation parameters developed in the first section
of this chapter. The statistics of the photodetector's output
(see figure 19) as a result of 100 simulations accurately ap-
proximates the analytical statistics. And the IAGC's response
(see figure 20) to the detector's output was correctly predic-
ted by the graphic analysis.
From these plots, the reduction in the signal variance
may not be apparent. Therefore, a signal to noise ratio will
be computed. The signal to noise ratio (SNR) is defined as
2 2SNR k 2k (54)
where
ak sample mean at time t
48
.0 -c
'oIi
SU)W
Ii " - i
I-are.g I .In~u
4C4... ..... ........ .... s 0
u T G IIuI uIII
49
> w
-,
U
atIs Gos go *9 e.a fSm8! 10 ) indino
Figure 20. TAGC Output
A-)25 and R=CO.Olnfe&)
3 sample variance at time tk
And an improvement factor (IMP) will be defined as:
IMP = SNR /SNR (55)y x
where
SNR = SNR of the AGC output
SNR x - SNR of the AGC input
An IMP > I would imply the AGC is reducing the shot noise ef-
fects. The IMP is plotted as a function of the input ensemble
average (see figure 21) which indicates the IAGC is reducing
the signal variance.
Varying the AGC parameters, A and G , does not effect the
general shape of the IAGC's response. Increasing G only0
provides greater amplification to the photodetector output
(see figures A-i and A-2). Increasing A decreases the am-
plification but provides better control of the si-nal fluctua-
tions (see figures A-3 and A-4). Varying the RC time con-
stant, on the other hand, causes transcient effects to become
noticable (see figures A-5 and A-6). As the RC approaches the
switching period, Ts, the IAGC begins to track the time or low
frequency components of the signal and becomes less sensitive
to input changes. When the reaction time becomes sufficiently
slow (RC T), the AGC loses its classification as an IAGC.
As apparent from the graphical analysis and through the
comparisione of the IAGC input-output simulations, the IAGC
51
p. -
;I
IAI
ILCHz
zww
0
00~ 000O 0M E 00-i 0ef0
Figure 21. Improvement of SNR by the IAGC
(IP-SHRout /SNR in)
52
does reduce the signal variance. By reducing the shot noise
effects the IAGC will improve the signal to noise ratio (SNR).
At first intution, an improved SNR would indicate that the
probability of error would decrease. For linear systems this
would be true, but AGC's have non-linear gain characteristics
which also shifts the energy levels.
Detector Pr(error) IAGC Parameters IAGC Pr(error)(with 90% certainty) G 0 A RC (with 90% certainty,
2x05 0.050+0.02254W105 0.048+0.022
6x105 125 0.01 0.048+0.0228x105 0.047+0.022
10x105 0.047;0.022
0.052+0.022 75 0.048+0.0225 100 0.048+0.022
6x10 5 125 0.01 0.0870.322150 0.047;0.022175 0.04770.022
0.01 0.048+0"022
0.05 0.050;0.0226x1O 5 125 0.1 0.052;0.025
0.5 0.083;0.0281.00 0.0+0.0
Table 2. Estimate of the Probability of a Bit Error for
an Initial Signal (binary one) Using an IAGC
- 5000 and 'D - 50000)
To analyze the effects of the IAGC on the probability of
error, again, requires a simulation of the receiver on the
computer. An estimate of the probability of a bit error is
shown in Table 2 for the first bit of received information
53
(binary one). A very weak optical signal and a large dark
current were needed to provide a non-zero estimate from the
1000 simulations. From the one-to-one input-output relation-
ship the graphical analysis predicted that the IAGC would have
no effect on the probability of error. As long as transients
are insignificant, the estimate is virtually unaffected by the
IAGC. As the RC time constant increases, the transients
become a factor in the detection process causing the
probability of error to increase.
XOt)
I I
I oI III I I
I I II I I I
xw - -__ 1- 1
T " one" ZT6 " ro'
Figure 22. Worst Case Signal
The influence of transients on the detection process is
more apparent for the "worst case" signal. This signal as-
sumes a frame interval of strong optical pulses are received
followed by a frame interval of pulses from a weak source (see
figure 22). The effects of the IAGC for various parameters is
shown by Table 3. As expected, increasing the RC time con-
stant slows the IAGC response, thereby, increasing the
54
probability of a bit error.
Detector Pr(error) IAGC Parameters IAGC Pr(error)(with 90% certainty) G A RC (with 90% certainty)0
2x105 0.062+0.0244x10 5 0.06270.0246xi0 5 125 0.01 0.064+0.0248x105 0.064;0.024I0xi0 0.064+0.024
0.052+0.024 75 0.062+0.0245 100 0.063+0.024
6x105 125 0.01 0.064+0.024150 0.064+0.024175 0.06470.024
0.01 0.064+0.0245 0.05 0.067+0.025
6xI0 125 0.1 0.069+0.0250.5 0.113+0.0311.0 0.204+0.040
Table 3. Estimate of Probability of a Bit Error for
the "Worst Case" Signal Using an IAGC
( = 5000 and D = 50000;• S D
for the previous pulse of kS=20000)
Based on the analysis one can obtain a feel for the ef-
fects of the IAGC on average probability of error. As long as
the IAGC has a quick response to input charges (RC << T ) thes
probability of a bit error is unaffected. But as RC in-
creases, the bit error increases causing the average
probability of error to increase. Although the IAGC does not
improve the probability of error, it does provide excellent
control to the signal fluctuations, and sufficient amplifica-
tion of the signal.
55
Receiver with an AGC
The most common purpose of the AGC's used today is to
control slow-time varying fluctuations that are super-imposed
on a signal. In this section an analysis is conducted to ex-
amine the effects of a common AGC in controlling the optical
signal fluctuations.
Simulation Parameters. For the analysis the photodetec-
tor parameters will be the same as those used in the previous
section. The AGC parameters will be obtained using similiar
methods but designed to control the fluctuations and to pass
the signal unaffected. For the particular signals being
analyzed, the fluctuations can be described as a change in the
DC component or the time average of the signal between the
frame periods (see figure 23). This "DC" signal will be
'I jI
j "I], 7111
Z Tr
Figure 23. Approximation to Describe Signal Fluctuations
used to compute the AGC parameters and to conduct an approx-
imate analysis of the AGC response.
56
The AGC will be designed to limit the DC output signal to
the range to 2mV to 4mV for an input DC signal that varies
between O.25PV and 25PV. The input values were obtained by
taking the time average of the photodetector's ensemble
averaged output. The 0.25uV corresponds to the time average
of the detector's output during the frame period that a weak
optical signal was received and the 25UV corresponds to the
frame period a strong optical signal was received. The output
range was arbitrarily chosen. Using these values in eqn (36)
and eqn (37), the AGC parameters, A and Go, are calculated to
be 2x1O 3 and 4x0 5 , respectively. The final AGC parameter,
the RC time constant, is restricted to the range T < RC < Tf.
This will insure that the AGC will be able to respond to the
signal fluctuations and not respond to the signal itself.
Analysis. Using the DC signal, an approximate analysis
can be conducted through the graphical techniques (see figure
24). The result of the graphical analysis indicates that the
AGC will reduce the range of the DC variations. Since the DC
level is directly proportional to the average signal; the
reduction in the variation of the DC level would imply that
the signal fluctuations will be reduced, assuming the signal
is not affected by the AGC. Because of the assumptions (the
AGC completely passes the signal and the filter only responds
to the DC level of a frame period), this graphical analysis is
only able to provide a "loose" approximation to the AGC
response.
57
In -
41
Figre 4. rapic nyi ofteACRs ne
---4- -~ 58
To obtain an accurate response, the receiver is implemen-
ted on the computer. Using the optical signal shown in figure
25, the photodetector's response (see figure 26) as a result
of the simiulation are analogous to the analytical statistics.
Using an RC - 4.Onsec, the AGC output (see figure 27) has very
noticable transient effects which distorts the photodetector
signal.
1.2
0.8
0.4
Figure 25. Input Optical Signal for a Receiver with an AGC
The effects of the AGC parameters produce similar results
in the performance of the receiver as they did for an IAGC.
Increasing the G provides greater amplification (see figures0
A-7 and A-8), and increasing the A provides better control of
the signal fluctuations (see figures A-9 and A-10). Like the
IAGC, the RC time constant has the greatest influence on the
AGC performance. Increasing RC insures the AGC tracks only
the DC component of a frame interval, but this also slows the
AGC's response to the changes in the DC level (see figures A-
59
INPUT *10r' (volts).00 0.03 0.08 0.09 0.12
C3
0
rgrnM
C:
totJ
Figure 26. AGC Input
63
OUTPUT *101 (voits).00 5.04 5308 0.12 0.16
om C
M1 -4
ma 0
m f0
Figure 27. AGC Output
(G 4x0,A-2000 and RC-4nsec)
61
11 and A-12) introducing transients. Decreasing RC increases
the AGC's reaction to DC charges but unfortunately also causes
the AGC to respond to the signal. Decreasing RC below T.
causes the AGC to be classified as an IAGC.
Detector Pr(error) AGC Parameters AGC Pr(error)(with 90% certainty) G A RC (with 90% certainty)
1105 0.657+0.0472xi05 0.240;0.0424x105 2000 4.0 0.079;0.0276x10 5 0.061+0.0248x105 0.055;0.023
0.0+0.0 1600 0.033+0.0181800 0.049+0.022
4x105 2000 4.0 0.079;0.0272200 0.158+0.0362400 0.298;0.046
2.0 0.072+0.0264.0 0.079+0.027
4x0 2000 6.0 0.156+0.0368.0 0.218+0.04210.0 0.241_0.043
Table 4. Estimate of the Probability of a Bit Error for
the "Worst Case" Signal Using an AGC
(kS . 10000 and XD = 50000;
for the previous pulse of X .20000)
The effects of the AGC on probability of error should
ideally be neglectible, because an AGC is to pass the signal
undistorted. But because of the transients, the AGC causes
the probability of error to increase as evident from Table 4
(for the "worst case" signal given in figure 22). Note, the
62
signal rate IS is larger in this analysis than in the IAGC
analysis. As apparent from comparing Tables 3 and 4, the AGC
has a greater detrimental effect on the average probability of
error even though it is designed not affect the signal.
Receiver with a Dual AGC
The analysis of the AGC's conducted thus far was limited
simple AGC configurations. In this section a simulation of a
dual AGC (two simple AGC's cascaded together) will be conduc-
ted. The compound AGC configuration will consist of an IAGC
followed by a common AGC. Because the IAGC has a quick
response, it will be able to control the large signal fluctua-
tions without affecting the probability of error. The AGC
will be able to provide further amplification of the signal
and provide greater control of the fluctuations. Since the
IAGC signifi.cantly decreases the dynamic range of the signal
fluctuation, the transient effect of the AGC on the probabili-
ty of error will be minimal.
The IAGC to be used in this compound configuration will
be the same as the IAGC that was studied in the first section.
The IAGC output is then used as an input to the AGC. The AGC
now designed to track the changes in the DC component of the
IAGC output instead of the photodetector's output. Using the
same method as developed in the previous section the AGC
parameters are computed to be A-0.5, Go=3200 and RC-4.Onsec.
Simulating this receiver produces an output shown in
figure 28, where the detector output is given in figure 26.
63
w to
I.> 10
0 aI
sg.- C0 01' 9f
Fiur 28 ua G Otu
CL64
As evident from figure 28 the dual AGC is able to provide con-
trol to the signal fluctuations and to provide ample gain to
the detector output. Since the dual AGC is two simple AGC's
cascaded together varying the parameters should produce the
same effects as they did for each of the separate AGC's.
Because of the time constraints, the plots of the dual AGC
ouput for various parameters could not be generated.
The effects that the dual AGC has on probability of error
is shown in Table 5 and Table 6. Through comparisons of Table
5 with Table 4, the probability of error is generally better
than the AGC alone. This is expected because the IAGC is able
to reduce the signal fluctuations, thereby, reducing detection
errors caused by the slow AGC response. Although comparing
Table 6 with Table 3, the AGC's slow response does still have
a detrimental effect on detection accuracy.
65
Detector Pr(error) IAGC Parameters AGC Parameters Dual AGC Pr(error)with 90% certainty GO A RC A RC with 90% certainty
2xi 05 0.027+0.01624xi0 5 0.08+0.00896x10W 125 0.01 3200 0.5 4 .003+0.0055
8xiOO 0.00370.0055
75 0.003+0.00555 00 0-0.0000055
6xI0" 125 0.01 3200 0.5 4 .003+0.0055150 0.007+0.0083175 0.01370.0113
0.,1 0.003+0.00550.05 0.006T0.0077
6x105 125 0.1 3200 0.5 4 0.008+0.00890.5 0.163T0.03691.0 0.550+0.04970.0+0.30___ _________
2400 0.027+0.0122
2800 0.007+0.00836xi05 125 0.01 3200 0.5 4 0.003+0.0055
3600 0.003+0.00554000 0.003+0.0055
0.40 0.000+0.00000.45 0.003+0.0055
6xI05 125 0.01 3200 0.5, 4 0.003+0.00550.55 0.014+0.0117O.6 0.057+0.0232
-.=10000 and 2 0.043+0.0203-' D 50 0 00 ; 4 0.003+0.0055
for previous 6xI0 125 0.01 3200 0.5 6 0.000+.0000
pulse of 8 0.000+0.0000x =20000) 10 o. ooo+-.0000S
Table 5. Estimate of the Probability of a Bit Error for
the "Worst Case" Signal Using a Dual AGC
66
Detector Pr(error) IAGC Parameters AGC Parameters Dual AGC Pr(error)with 90% certainty G A RC G A RC with 90% certainty
0 0
52xI05 0.309+0.04624x1O5 0.16970.03756x105 125 0.01 3200 0.5 4 0.10370.03048X10l 0.070+0.025510x10 0.055+0.0228
75 0.053+0.0224100 0.0650.0247
6xIO 5 125 0.01 3200 0.5 4 J.10370.0304150 0.15570.0362175 0.21370.0409
0.01 0.103+0.03040.05 0.107'0.0309
6x105 125 0.1 3200 0.5 4 0.135+0.03420.5 0.39670.04891.0 0.782+0.0413
0.063+0.024 ___
2400 0.245+0.04302800 0.158+0.0346
6x105 125 0.01 3200 0.5 4 0.1030.03043600 0.069+0.02534000 0.055+0.0228
0.40 0.013+0.01130.45 0.0407+0.0196
6xi05 125 0.01 3200 0.50 4 0.103+0.03460.55 0.229F+0.04200.60 0.456+0.0498
(X15000 and 2 0.330+0.0471I D5 0000; 5 4 0.103+00304for previous 6xiO 5 125 0.01 3200 0.5 6 0.039+0.0194pulse of 8 0.021+0.0143S -20000) 0 0.0170.0129
Table 6. Estimate of the Probability of a Bit Error for
the "Worst Case" Signal Using a Dual AGC
67
VI. Conclusions and Recommendations
Conclusions.
The purpose of this paper was to analyze the effects of
an AGC in an optical receiver. The particular optical signal,
which was studied, was a Manchester coded digital signal with
varying optical power densities. The optical signal was con-
verted into an electrical signal by a photodetector. Inserted
after this detector was an AGC with the intent of improving
the performance of the receiver. The criteria to assess the
AGC's effects on the receiver's performance were:
I) amplification of the detector signal
2) control of the signal fluctuations
3) improve the detection accuracy.
Using this criteria three specific AGC's were analyzed.
From the analysis, an AGC which has a quick response was
determined to be the most suitable for the optical receiver.
Although a quick AGC response causes distortion of the
photodetector output, the decision criteria was not effected
by the addition of the AGC's. Of the three AGC's examined,
the IAGC had the fastest reaction to input changes (as long as
RC<<T ). The IAGC was able to provide amplification of the
signal and to control signal fluctuations, but it had no sig-
nificant effect on the probability of error. Because of their
slow response, the other AGC's that were studied caused an
68
increase in probability of error. The IAGC was able to
provide amplification of the signal and control signal fluc-
tuations, but it had no significant effect on the probability
of error. Thus, an AGC in an optimal receiver is not capable
of improving the probability of error. Although this is not
the result which is desired, it is an intuitively pleasing
result. Having a device (which controls the signal amplitude)
improve the accuracy of PPM detection would not have been an-
ticipated.
Although the AGC will not improve the detection accuracy,
it can be used to amplify the signal and to control the signal
fluctuations. For signals with a wide dynamic range of fluc-
tuations, using an AGC in the receiver may be more applicable
than a constant gain amplifier. Since the AGC had non-linear
gain characteristics, it can be use to provide ample gain to a
weak signal to simplify the detection process. And during the
reception of a strong signal the AGC will automatically reduce
the gain to prevent saturation of the decision circuitry.
Therefore, circuit limitations may require the use of an AGC,
even though an AGC will not improve the probability of error.
Recommendations
Because of the numerous possible AGC configurations and
time constraints, only three AGC's were examined, therefore
the analysis could be expanded to investigate other AGC
models. Since the AGC's can not improve the detection ac-
curacy, the study should be focused on minimizing an increase
69
in the probability of error, while maintaining that the AGC
still provide sufficient amplification of the signal and con-
trol of the fluctuations.
Other photodetector models could also be analyzed. In
this paper the photodetector was modelled as a weighted Pois-
son counting process. This required a large RC time constant
(compared to the signal bandwidth) and the implementation of a
switch. Using a large RC time constant caused the signal in-
formation to be lost and an impracticable switch had to be
implemented to obtain the information sent. Therefore, a more
accurate photodetector model could be investigated by
eliminating the switch, which would require the RC time con-
stant in the detector model to be reduced.
The analysis could also be expanded to examine other op-
tical signals and channels. A study of optical signals which
are transmitted through the atmosphere may be more adaptable
to AGC control. The atmospheric turbulance will cause the
signal to incur continuous time varying fluctuations, unlike
the discrete fluctuations caused in the fiber optic system
which das analyzed. With the continuous time-varying fluctua-
tions the AGC will not be required to have a quick response.
This will enable the use of AGC's which are commonly used
today.
70
in the probability of error, while maintaining that the AGC
still provide sufficient amplification of the signal and con-
trol of the fluctuations.
Other photodetector models could also be analyzed. In
this paper the photodetector was modelled as a weighted Pois-
son counting process. This required a large RC time constant
(compared to the signal bandwidth) and the implementation of a
switch. Using a large RC time constant caused the signal in-
formation to be lost and an impracticable switch had to be
implemented to obtain the information sent. Therefore, a more
accurate photodetector model could be investigated by
eliminating the switch, which would require the RC time con-
stant in the detector model to be reduced.
The analysis could also be expanded to examine other op-
tical signals and channels. A study of optical signals which
are transmitted through the atmosphere may be more adaptable
to AGC control. The atmospheric turbulance will cause the
signal to incur continuous time varying fluctuations, unlike
the discrete fluctuations caused in the fiber optic system
which was analyzed. With the continuous time-varying fluctua-
tions the AGC will not be required to have a quick response.
This will enable the use of AGC's which are commonly used
today.
70
Bibliography
1. Davenport, William B. Jr. Probability and RandomProcesses. New York: McGraw-Hill Book Company, 1970.
2. Deffebach, H. L. and W. 0. Frost. A Survey of DigitalBaseband Signalling Techniques. Alabama: GeorgeC. Marshall Space Flight Center, June 1971.
3. Gagliardi, Robert M. and Sherman Karp. Optical Communica-tions. New York: Wiley-Interscience Publication,1976.
4. Hornbeck, Robert W. Numerical Methods. New York: QuantumPublishers, Inc., 1975.
5. Kleekamp, Charles and Bruce Metcalf. Designer's Guide toFiber Optics-Parts 1-4. Summary of Optical FiberSystems. Boston: Cahners Publishing Company, 1978.
6. Melsa, James L. and David L. Cohn. Decision and EstimationTheory. New York: McGraw-Hill Book Company, 1978.
7. Oliver, B. M. "Automatic Volume Control as a FeedbackProblem," Proceedings of the IRE, 36:466-473 (April1948).
8. Papoulis, Anthanasios. Probability, RandoL Variables andStochastic Processes. New York: McGraw-Hill Book Com-pany, 1965.
9. Senior, Edwin W. Automatic Gain Control Theory for Pulsedand Continuous Signals. A Comprehensive Study ofAGC's. Stanford: Stanford Electronic i-boratories,June 1967. (AD 825 380).
10. Snyder, Donald. Random Point Process. New York: Wiley-Interscience Publication, 1975.
11. Solymar, Laszio and Donald Walsh. Lectures on the Elec-trical Properties of Materials (Second Edition).Oxford: Oxford University Press, 1979.
12. Williams, N. A. F. "Automatic Gain Control Systems," Wire-less World, 83:60-1 (September 1977).
13. Ziemer, R. E. and W. H. Tranter. Principles of Communica-tions. Boston: Houghton Mifflin Company, 1976.
71
fb
Appendix A
Graphs of Various AGC Responses
This appendix contains plots of the AGC response to a
given optical input for various AGC parameters. The plots are
presented in pairs in which one AGC parameter is varied
between the pair. This will enable the reader to compare the
effects that the parameter has on the photodetector output.
The photodetector output for the first six graphs is
given in Figure 19 and the last six in figure 26. Each graph
contains a plot of the mean + 100 standard deviations, which
is a result of 100 simulations.
72
0 Lq0
UU
coo
Is,
2T 9000 6060 W
c~(so, d n
FiueA1 IC u)~ w t 2l
(A15an COglscuw73
a.
>NU)
0WOW
1> *
OWO
isi
at "l 0110 90"0 1 00 £8(s,ToA) lndino
Figure A-2. IAGC Output with G 0,-3xO5
0
(A-125 and RC-O.O1nsec)
74
H) -
> D
H> 1 2
0 W
UI W
800 900<STA ifd)l
Figur A-3 IAG wit AM3
6C
(00=6x13 and RC-O.Olnsee)
75
-W
3
U)
H>4
00
89 M0
aa
vj.
0 M,nmm:o-3 *
U
Lcd
8080 900 t 0 z 0 o
Figure A-4. IAGC Output with A-150
(C .6xlO5 and RC-0.O1nsec)
76
WU4-34
U) >
102
0.0W
U - +U, (X o-< Wa
8669 90 *0 V90 0 040
Figure A-5. TAGC Output with RCm0.inseo
(G m6xi3 5 and A-125)
77
I td
W
a. -
>u us*u~ou(80A LlJfO--
(B 6x10 andA1no
78
LL
aI-
Low(-,-
UaI
c))
9 go t0 8000 r 0 o 00'
Figure A-7. AGC Output wit1,. G xI0
(A-2000 and RCm-0nsec)
79
4-d
Ca
IL.
90 890 to iPZ)~oA cr* fd-l
aC0A20 and RC4Ormc
U8
1-41-- 0
HDfi
U)~~A F-1 flil
(G 241UadRC4Osc
>
C i aC) 81
CL?
W F-1
> -
F->
o WLY-Uw+'
aC
2100 80 10 o1000
FIgure A-10. AGC Outpu1t with A*2200
(G 0 4xlO an4 RC-4.0nsec)
832
AD-A124 696 IMPROVED SIGNAL CONTROL AN ANALYSIS- 0THE EFFECTS 0OF 2A UTMAT GAINCON.U) AIR FORCE INS 0 FECH7 A WR11 GH P IATERS ON AF R OH SCHOOL OF ENDI. K L IER
UNCLASSFED EC 82 AF TGED EE/R2D 3 F 072 N
III~lIgo
L 6
1 125 [.4 Q
MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDYS-1963-A
IM
I LiJ u
CM
0 L
09 006
0I x
02
CY
'U'
U -;
Qz 4 002 0 T. 0. o
IfolL* ini
(G0 9 4l n m00 uP
84
b
Appendix B
Computer Program
This appendix contains the program which was used to
generate the data for the plots and the tables provided in
this report. The program is written in FORTRAN IV programming
language and implemented on the CDC 6600 computer system. The
uniform random number generator subroutine is not presented
here. This routine was obtained from the INSL library which
was available at AFIT.
85
1oom PROGRAM DUAL(INPUT,OUTPUT,TAPE5-INPUT ,TAPE6-INPUT.TAPE1.110- *TAPE2,TAPE3,TAPE4,TAPE7,TAPE8)120- DIMENSION xl(1oo0),Yl(1oo),V1(10o)),Tl(lO),'r2(1oo),R(2),XLA?4DA(31)
*130- *,YT(100),XT(100),Y2(100),V2(l00)140- DOUBLE PRECISION DSEED150- INTEGER COUNTI ,COUNT2
* 160-C170-C180-C190-C INITIAL SEED FOR RANDOM NUMBER GENERATION :200-C210- DSEED-92751220-C230-C240-C NUMBER OF SIMULATIONS OF A GIVEN OPTICAL SIGNAL250-C260- NRUN=100270-C
290-C INPUT OPTICAL SIGNAL GIVEN IN TERMS OF THE SIMULATION RATES300-C :uTHESE RATES WERE ARBITRARILY CHIOSEN BY THE PROGRAMER310-C320- XLAMDA()=0.0330- XLADA(2)=100.0340- XLANDA(3)-100.0350- XLAKDA(4-0-0360- XLANDA(5)-100.0370- XLAMDA(6)-0.0380- XLAMDA(7)-103.0390- XLAMDAC8)-O.0400- XLAMDA(9)=0.0410- XLAMDA(10)-100.0420- XLAMDA(11 )-8oo.o430- XLAMDA(12)-0.0440- XLAMDA(13)-800.O450- XLAMDA(14)-0.0460- XLAXDA(15)-0-0470- XLANDA(16)-WO.0480- XLAMDA(17)-0.0490- XLAMDA(18)-800.O500- XLAMDA(19)-0.3510- XLADA(20)-800.0520- XLAMDA(2)-200.0530- XLAMDA(22)-0.0540- XLAMDA(23)-0.0550- XLAMDA(24)-200.0560- XLANDA(25)-0.0570- XLANDA(26)-200.0580m XLANDA(27)-0.0590- XLAMDA(28)-200.0600- XLAKDA(29)-0.0610- XLAKDA(30)0200.0
86
630-C SIMULATION RATE OF THE THERMALLY EMITTED ELECTRONS *640-C650- DARK-10.0660-C670-C680-C690-C (Q/C)*N - CONSTI - WEIGHTING FACTOR FOR THE COUNTING PROCESS700-C TO PRODUCE AN ACCURATE REPRESENTATION OF THE DETECTOR ***
710-C720- CONSTI-1 .OE-8730-C740-C750-C760-C770-C780-C 4 AGC PARAMETERS790-C800-C810-C * AGC PARAMETERS FOR THE FIRST AGC (IAGC)820-C830- RC-0.01840- G-600000.0850- A-125.0860-C870-C880-C A AGC PARAMETERS FOR THE SECOND AGC (COKON AGC) *890-C900- RC2-10.0910- A2-0.5920- G2-3200.0930-C940=C950-C960-C970-C
990-C , TINE PARAMETERS (UNITS ARE RELATED TO THE BAUD RATE)1000-C1010-C1020-C1030-C ' PERIOD OF THE SWITCH (CLOCKING PERIOD) *U41040-C u THIS PERIOD - 1/2 THE BIT PERIOD1050-C1060- PERIOD- 1.01070-C1080-C COMPUTER SAMPLING INTERVAL1090-0C1100- DELTA-0.0011110-c
1120-C1130-1C ' NUMBER OF CLOCK PERIODS TO SIMULATED1140-C11i50- NPER04
87
I.
r 1170-C
1180-C * NUMBER OF SAMPLES PER CLOCK PERIOD1190-C1200- NSAM=P-INT( (PERIOD+O. ooo001 )/DELTA)1210-C1220-C1230-C THE J-TH SAMPLE AT WHICH THE STASTICS ARE COMPUTED *
1240-C1250- JSAMP-501260-C1270-C1280-C m THE BIT PERIOD AT WHICH PROB(ERROR) IS COMPUTED1290-C1300-C CLOCK PERIOD FOR THE FIRST HALF OF THE BIT PERIOD1310= NPERI-51320-C CLOCK PERIOD FOR THE SECOND HALF OF THE BIT PERIOD1330- NPER2-61340-C1350-C1360-C1370-C1380-C1390-C1400-C *.* INITIALIZE PARAMETERS .'1410=C1420=C1430-C1440- DO 10 K-I ,NRUN1450- TI(K)=O.O1460- T2(K)-O.O1470- Xl(K) 0.01480- V2(K)=O.O1490- Vl(K)-O.O1500-10 CONTINUE1510-C1520-C1530-C1540-C1550-C .:z BEGIN SIMULATION1560-C1570- DO 400 I-i ,NPER1580-C1590-C1600- JTH-I1610- COUNTIO1620- COUNT2-01630-C1640-C1650-C NUN SIMULATE ONE CLOCK PERIOD tUS1660-C1670- DO 300 J-1,NSAMP1680-C1690- TIME-DELTA*FLOAT(J)
saL
1710-C COMPUTE THE DETECTOR VOLTAGE, AGC OUTPUT VOLTAGE, AGC1720-C CONTROL VOLTAGE FOR EACH RUN *1730-C1740- DO 100 K1, NRUN1760-C1 770-C1780-C GENERATION OF A COUNTING PROCESS TO SIMULATE AN IDEAL DETECTOR1790-C1800-C1810- IF (XLAMDA(I).EQ.0.0) GOTO 301820- COUNT1-01830-C1840-C Tl(K) IS THE TIME AT WHICH M ELECTRONS ARE EMITTED FROM THE1850-C IDEAL PHOTODECTOR AS A RESULT OF THE INCIDENT OPTICAL SIGNAL1860-C1870-20 IF(T1(K).GT.TIME) GOTO 301880-C GGUBS - IMSL UNIFORM NUMBER GENERATOR SUBROUTINE1890- CALL GGUBS(DSEED,2,R)1900-C GENERATE A NEW SEED1910- DSEEDR(2)*123457.01920-C1930-C CONVERT UNIFORM NUMBER INTO A EXPONENTIAL RANDOM NUMBER1940- TAU1 --ALOG(R(1 ))/XLAMDA(I)1950-C INCREMENT COUNT; ONE COUNT IS EQUIVALENT TO M PHOTON TO1960-C ELECTRON CONVERSIONS1970- COUNTI -COUNTI +11980-C TIME AT WHICH X PHOTON TO ELECTRON CONVERSIONS OCCUR1990- TI ()-TI (K)+TAUI2000- GOTO 20201 0-30 CONTINUE2020-C INITIALLY ONE COUNT TO MANY IS GENERATED2030- IF((J.EQ.i).AND.(COUNT1.NE.0)) COUNTI-COUNT1-12040-C2050-C2060-C u GENERATION OF COUNTING PROCESS TO ADD DARK CURRENT EFFECTS ***
2070-C2080C2090=C2100-C THESE PARAMETERS ARE SIMILAR TO THOSE DESCRIBED IN THE2110-C IDEAL SIMULATION2120-C2130- IF(DARK.EQ.0.0) GOTO 502140- COUNT2-02150-40 IF(T2(K).GT.TIME) GOTO 502160- CALL GGUBS(DSEED,2,R)2170- DSEED-R(2)0123457.02180- TALJ2--ALOG(R(1 ))/DARK2190- COUNT2-COUNT2+12200- T2(K)-T2(K)+TAU22210- GO TO 402220-50 CONTINUE2230- I1((J.EQ.I ).AND.(COUNT2.NE.o)) COUNTZ-COUNT2-1
89
2240-C2250-C ' PHOTODETECTOR SIMULATION2260-C2270-C2280- Xl (K)-CONSTI*PLOAT(COUNTI+COUNT2)+XI (K)2290-C2300-C2310-C2320-C2330-C ** DUAL AGC SIMULATION 1
2340-C2350-C2360-C2370-C IAGC OUTPUT VOLTAGE2380- YI (K)=x1 (K)*G*EXP(-(A*v (K)))2390-C IAGC CONTROL VOLTAGE240o- Vi (K)-(YI (K)-vI (K))*DELTA/RC+Vl (K)2410-C AGC OUTPUT VOLTAGE2420- Y2(K)"YI (K)*G2*EXP(-(A2*V2(K)))243 0-C AGC CONTROL VOLTAGE2440- V2(K)-(Y2(K)-V2(K)) DELTA/RC2+V2(K)2450-100 CONTINUE2460-C2480-C2490-C2500-C2510-C *4***. .4,:Ee14I42520-C . COMPUTE STATISTICS2530-C2540-C2550-C2560-C CALCULATE STATISTIS FOR EVERY J-TH SAMPLE2570-C2580- IF(JTH.NE.JSAMP) GOTO 2002590- JTH-O2600- SUMN -0.02610- SUM2-0.02620- 5 O.3-0.02630- SUM4-0.02640- SU5-0.02650- SUM6-0.02660-C2670-C2690-C2700-C COMPUTE MEAN III
2710-C2720- DO 60 K-I,NRUN2730- 811(1 -SUMl+Xl (K)2740- SUJM2-SU2+YZ(K)2750-60 CONTINUE2760-C2770- XMN-SUMI /LOAT(NRUN)2780- YKN-SU?2/FLOAT(NRUN)
90
2800-C COMPUTE VARIANCE 42810*C2820- DO 70 K-1 , NRUN2830- SUM3-SU3+(XN-Xl (K))**22840- SUM4-SUM4+(YMN-Y1 (K))22850-70 CONTINUE2860-C2870- XVAR-SUM3/FLOAT( NRuN)2880- YVAR-SUM4/FLOAT (NRUN)2890-C2900-C2910-C2920-C2930-C ' COMPUTE SIGNAL TO NIOSE RATIOS **-
2940=C2950- SNRX-XMN2/XVAR2960- SNRY=YMN**2/YVAR2970-C2980-C2990-C3 "0-C * IMPROVEMENT FACTOR *3310-C3020- IP-SNRY/SNRX3030-C3040-C3050-C3060-C3070-03080-C WRITE ONTO TAPE NEEDED DATA ***
3090-C3100- WRITE(1,*) XMN,XVAR3110- WITE(7,*) YMN,YVAR3120-C3130-C r3140-2W CONTINUE
3150-C3160- IF(JSAMP.GT.i) JTH-JTH+i3170-C3180-C3190-300 CONTINUE3230-C3 2 4 0 -6 = = = = = : = = : = : : = : = : = = m * H
3250-C :uu COMPUTE THE PROBABILITY OF ERROR **
3260-C ,14 =4 ===4 * .3270-C3280-C3290a IF(NPER.N.NPERI) GOTO 723300- DO 71 JIC-i,MUN3310- XT(JI)-X1(JK)3320- YT(JK)-Y2(JK)3330-71 CONTINUE3340-C3350-72 CONTINUE
91
,
3393-C 4dTHIS ROUTINE WILL ONLY COMPUTE THE PR(ERROR)3400-C FOR A BINARY "ONE" 44
3410-C3420- IF(NPER.NE.NPER2) GOTO 75343- SUM-0.03430- SUMi -0.03450- SUM3O0.03460- SUM4-0.03470-C3483)-C [3490- DO 74 JK-1 ,NRUN3500- IF(X1 (JK).GT.XT(JK)) SUMi=SUM1., .3510- IF?(XI(JK).EQ.XT(JK)) SUM2-SUM2+0.53520= IF(Y2(JK).GT.YT(JK)) StM3-SUM3+1 .03530- IF(Y2(JK).EQ.YT(JK)) SUM4=SUM4+0.53540-74 CONTINUE3560-C3570-C3580-C COMPUTE A PROBABILITY OF ERROR FOR THE INPUT3590- PRX-(SUM1 +SUM2)/FLOAT(NRUN)36,)0C3610-C COMPUTE A PROBABILITY OF ERROR FOR THE OUTPUT3620- PRY-(SUM3+SUM4) /FLOAT(NRUN)3630-C3650-C3660-C3670-C COMPUTE THE VARIANCE OF THE INPUT PR(ERROR)3680- PRXVAR- (SUMI4'( 1.0-PRX)4 '*2+SU424(.5-PRX)**2) /FLOAT(NRUN)3690- PRXVAR-PRX'VAR+(t .O-PRX)*PRXt4'23700-C3710-C COMPUTE THE VARIANCE OF THE OUTPUT PR(ERROR)3720- PRYVAR-(SU43*(1 .O-PRY)*2+SUr.4*(o.5-PRY)**2)/FLOAT(NRUN)3730- PRYVAR-PRYVAR.(1 .3-PRY)' PRY' 4 23740-C3750-C3760-75 CONTINUE3770-C3790-C3800-C3810-C ~'RE-INITIALIZE PARAMETERS ~43820-C3830- DO 80 K-I,NRUN3840- Xl(K)-O.O3850- Tl(K)-0.03860m T2(K)-O.O3870-80 CONTINUE3880-C3890-C3900-400 CONTINUE3910-C3953- STOP3960- END3973-4'NOE
92
II
VITA
Kirk Lee Fisher was born 8 December 1959 in New Columbia,
Pennsylvania. He graduated from High School in 1977 and at-
tended the Pennsylvania State University from which he
received a Bachelor of Science in Electrical Engineering in
May 1981. During the first two years he attended the Hazelton
Branch Campus and upon entering University Park Campus he ac-
cepted a scholarship through the Air Force Reserve Officer
Training Corps. In June of 1981 he entered the School of
Engineering at the Air Force Institute of Technology to obtain
a Master's of Science. He is a member Eta Kappa Nu, Tau Beta
Pi and Institute of Electrical and Electronics Engineers.
Permanent Address: Box 393 RD # INew Columbia, Pennsylvania
17856
93
UNCLASSIFIEDSECURITY CLASSIFICATION of "rtNi 0 5 " noflate. Cr.tered)
REPORT DOCUMENTATION PAGE RFAD INSTRUCTIONSREPORT__DOCUMENTATION__PAGE______BEFGrE COMPLETING FORM
I. REPORT NtUMbDER 2. GOVT ACCESSION NO. 3. PECI'FIvT"; CATALOG NUMBER
AFIT/CEO/EE/82D-3 1____________4. TITLE (and Subtitle) S. TIFE aF REPORT & PERIOD COVERED
IMPROVED SIGNAL CONTROL: AN ANALYSIS OF THE MS Thesis
EFFECTS OF AUTOMATIC GAIN CONTROL FOR
OPTICAL SIGNAL DETECTION s. PERFORMING ORG. REPORT NUMBER
7. AUTHOR(.' B. CONI RACT OR GRANT NUMBER(s)
K":k L. Fisher
9. PERFORMING ORGANIZATION NAME AND AODRESS 10. PPOGPAM ELEMENT. PROJECT, TAS,APEA A WORK UNIT NUMBERS
Air Force Institute of Technology (AFIT-EN)
Wright-Patterson AFB, Ohio 45433
It. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Dec, 198213. NUMBEP OF PAGES
9314. MONITORING AGENCY NAME & ADDRESS(It differeit from Controlling Office) IS. SECURITY CLASS. (ot this report)
IS*. DECLASSIFICATION/DOWNGRADINGSCHEDULE
IS. DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited
17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20. it different from Report)
IS. SUPPLEMENTARY NOTES Wg ...... g" - ..... . 4
f atse Isttute ct lcn.! -'j (ATC)
19. KEY WORDS (Continue on reverse aide It necessary and Identify by block number)
Automatic Gain ControlOptical CommunicationSignal DetectionFiber Optics
20. ABSTRACT (Continue an reverse olde If neceesary and Identify by block number)
This paper is to analyze the effects of an automatic gain
control (AGC) in an optical receiver system. The intent of
using an AGC is to improve the performance of the receiver.
The received signal is Manchester encoded and nontains
fluctuations caused by transmission attenuation. In the con-version from an optical signal to an electrical signal, the
photodetector produces shot noise. The purpose of the AGC
DNO 1473 EDITION OF I NOV G IS OBSOLTE UNCLASSIFIED
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UNCLASSI FIEDSECURITY CLASSIFICATION OF THIS PAGE(hou Date Enteted)
will be to amplify the photodetector signal, control signalfluctuations, reduce shot noise, and improve detection ac-curacy.
Using this criteria, 4is effects of the ACC in thereceiver was examined. But because of the non-linearitiesassociated vtth an AGC, an analytical analysis can not be con-
ducted. Therefore, the receiver was simulated on the com-puter. This paper describes the models and algorithms used toanalyze the receiver. Through the simulations, the receiver'sperformance with an AGC is compared to the performance withoutan AGC.
Because of the limited time for the analysis, only threespecific AGC's were examined. The first AGC studied is clas-sified as an instantaneous AGC (IAGC) followed by an analysisof a common AGC. The final AGC to be investigated is a dualAGC which is an AGC cascaded to an IAGC.
UNCLA~s FTrnSCCURITY CLASSIFICATION OF THIS PAGE(ftmn De Bnk80
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the'ies,on-lom-I t oIar 9riouthreelas-ysisdual
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